A306212 Numbers that are the sum of squares of three distinct positive integers in arithmetic progression.

14, 29, 35, 50, 56, 66, 77, 83, 93, 107, 110, 116, 126, 140, 149, 155, 158, 165, 179, 194, 197, 200, 210, 219, 224, 242, 245, 251, 261, 264, 275, 290, 293, 302, 308, 315, 318, 332, 341, 350, 365, 371, 372, 381, 395, 398, 413, 428, 434, 435, 440, 450, 461, 462, 464, 482

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

35 = 1^2 + 3^2 + 5^2, with 3 - 1 = 5 - 3 = 2;
371 = 1^2 + 9^2 + 17^2, with 9 - 1 = 17 - 9 = 8. Also 371 = 9^2 + 11^2 + 13^2, with 11 - 9 = 13 - 11 = 2.

Maple

N:= 1000: # for terms <= N
S:= {seq(seq(3*a^2+2*b^2, b=1..min(a-1, floor(sqrt((N-3*a^2)/2)))), a=1..floor(sqrt(N/3)))}:
sort(convert(S, list)); # Robert Israel, Jun 08 2020

Prog

(PARI) for(n=3, 600, k=sqrt(n/3); a=2; v=0; while(a<=k&&v==0, b=(n-3*a^2)/2; if(b==truncate(b)&&issquare(b), d=sqrt(b); if(d>=1&&d<=a-1, v=1; print1(n, ", "))); a+=1))
(PARI) w=List(); for(n=3, 600, k=sqrt(n/3); for(a=2, k, for(c=1, a-1, v=(a-c)^2+a^2+(a+c)^2; if(v==n, listput(w, n))))); print(vecsort(Vec(w), , 8))

Crossrefs

Cf. A000290, A000378, A000408, A085317, A120328, A292313, A306213, A306214.

Sequence in context: A174070 A045527 A353197 * A041384 A041382 A047725

Adjacent sequences: A306209 A306210 A306211 * A306213 A306214 A306215

Keyword

nonn

Author

Antonio Roldán, Jan 29 2019

Status

approved